Within the university, Kenny was Wilde Lecturer in Natural and Comparative Religion (1969–72), Speaker's Lecturer in Biblical Studies (1980–83), a member of the Hebdomadal Council (1981–93), Vice-Chairman of the Libraries Board (1985–88), Curator of the Bodleian Library (1985–88) and a Delegate, and member of the Finance Committee, of Oxford University Press (1986–93). From 1972 until 1973 he was the editor of The Oxford Magazine. He received the degree of DLitt in 1980 and the honorary degree of DCL. in 1987.

He was a member of the Board of the British Library 1991-96 and Chairman 1993-96, and has served as Chairman of the Society for Protection of Science and Learning (1989–93), of the British National Corpus Advisory Board (1990–95), of the British Irish Association (1990–94), and of the Board of the Warburg Institute (1996–2000). He was elected a Fellow of the British Academy in 1974 and served as a member of the Council of the Academy 1985-88, as Vice President 1986-88 and President 1989-93.

Although deeply interested in traditional Catholic teaching and continuing to attend the Catholic Mass,[4] Kenny now explicitly defines himself as an agnostic, explaining in his What I believe both why he is not a theist and why he is not an atheist. His 2006 book What I believe has (as Ch 3) "Why I am Not an Atheist" which begins: "Many different definitions may be offered of the word 'God'. Given this fact, atheism makes a much stronger claim than theism does. The atheist says that no matter what definition you choose, 'God exists' is always false. The theist only claims that there is some definition which will make 'God exists' true. In my view, neither the stronger nor the weaker claim has been convincingly established". He goes on "the true default position is neither theism nor atheism, but agnosticism ... a claim to knowledge needs to be substantiated; ignorance need only be confessed."[5] He defends the rationality of an agnostic praying to a God whose existence he doubts, stating "It surely is no more unreasonable than the act of a man adrift in the ocean, trapped in a cave, or stranded on a mountainside, who cries for help though he may never be heard or fires a signal which may never be seen."[6] This view is kin to Christian agnosticism.

Kenny has written extensively on Thomas Aquinas and modern Thomism. In The Five Ways, Kenny deals with St. Thomas' five proofs of God. In it, Kenny argues that none of the proofs Thomas sets out are wholly valid, and instead, sets out to show the flaws in the five ways. His arguments range from the problem of Aristotelian motion in a modern scientific context, to the ability of contingent beings to cause eternality in other contingent beings. His objections all focus on a modern interpretation of St. Thomas.

Kenny candidly describes the predicament of the beginning of the universe, both an atheist and agnostic faces, writing, "According to the Big Bang Theory, the whole matter of the universe began at a particular time in the remote past. A proponent of such a theory, at least if he is an atheist, must believe that the matter of the universe came from nothing and by nothing."[7]

In What is Faith?, Kenny addresses "the question of whether belief in God, and faith in a divine world, is a reasonable or rational state of mind."[8] He criticises the idea, "common to theists like Aquinas and Descartes and to an atheist like Russell," that "Rational belief [is] either self-evident or based directly or indirectly on what is evident" which he terms "foundationalism" following Plantinga[9] arguing out that foundationalism is a self-refuting idea.